Finite Group Databasebeta

← C2×C5×D4×C3⋊D3 #13089492

Subgroups — C2×C5×D4×C3⋊D3 #13089492

Order 1440.

1416 conjugacy classes of subgroups; only the 346 normal subgroups are shown.

normal subgroups only

This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 346 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C3⋊D3C212yesmaximal, complemented
2C2×C32×C5×D4C211yesmaximal, characteristic, complemented
3C2×C5×#638C212yesmaximal, complemented
4C5×D4×C3⋊D3C218yesmaximal, direct product factor
5C2×C5×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
6C2×C4×C5×C3⋊D3C211yesmaximal, characteristic, complemented
7C2×C5×D3×D4—34nomaximal
8C23×C32×C5C2212yescomplemented
9C22×C5×C3⋊D3—28no—
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C5×C3⋊D3C2218yescomplemented
12C22×C5×C3⋊D3C2212yescomplemented
13C32×C5×D4C2214yescomplemented
14C2×C32×C4×C5C2211yescharacteristic, complemented
15C5×#638C2218yescomplemented
16C2×C5×C3⋊Dic3C2211yescharacteristic, complemented
17C5×C4⋊(C3⋊D3)C2214yescomplemented
18C4×C5×C3⋊D3C2214yescomplemented
19C2×D4×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
20C23×C5×D3—38no—
21C2×C3×C5×D4D314yescomplemented
22C2×C5×#67—38no—
23C5×D3×D4—332no—
24C2×C5×D12—34no—
25C2×C4×C5×D3—34no—
26C22×C32×C5—24no—
27C22×C32×C5C2311yescharacteristic
28C22×C32×C5C2314yescomplemented
29C2×C5×C3⋊D3—24no—
30C2×C5×C3⋊D3—216no—
31C2×C5×C3⋊D3D414yesdirect product factor
32C2×C5×C3⋊D3C2312yes—
33C2×C5×C3⋊D3C2314yescomplemented
34C32×C4×C5C2312yescomplemented
35C5×C3⋊Dic3C2312yescomplemented
36C22×C5×D4—91noHall
37C23×C3⋊D3C2×C512yescomplemented
38C2×C32×D4C2×C511yescharacteristic, complemented
39C2×#638C2×C512yescomplemented
40D4×C3⋊D3C2×C518yesdirect product factor
41C2×C4⋊(C3⋊D3)C2×C511yescharacteristic, complemented
42C2×C4×C3⋊D3C2×C511yescharacteristic, complemented
43C23×C3×C5C2×D318yescomplemented
44C22×C5×D3—34no—
45C22×C5×D3—38no—
46C22×C5×D3—332no—
47C22×C5×D3—632no—
48C3×C5×D4C2×D3116yescomplemented
49C2×C3×C4×C5C2×D314yescomplemented
50C5×#67—332no—
51C2×C5×Dic3—34no—
52C5×D12—316no—
53C4×C5×D3—316no—
54C2×D3×D4—34no—
55C2×C32×C5—24no—
56C2×C32×C5C2×D412yescomplemented
57C2×C32×C5C2411yescharacteristic
58C5×C3⋊D3—24no—
59C5×C3⋊D3C2×D414yesdirect product factor
60C24×C5—92no—
61C2×C5×D4—92no—
62C2×C5×D4—98no—
63C2×C5×D4—91no—
64C2×C5×D4C3⋊D311yescharacteristic, direct product factor
65C22×C4×C5—91no—
66C23×C32C22×C512yescomplemented
67C22×C3⋊D3—28no—
68C22×C3⋊D3C22×C511yescharacteristic
69C22×C3⋊D3C22×C518yescomplemented
70C22×C3⋊D3C22×C512yescomplemented
71C32×D4C22×C514yescomplemented
72C2×C32×C4C22×C511yescharacteristic, complemented
73#638C22×C518yescomplemented
74C2×C3⋊Dic3C22×C511yescharacteristic, complemented
75C4⋊(C3⋊D3)C22×C514yescomplemented
76C4×C3⋊D3C22×C514yescomplemented
77C22×C3×C5—216no—
78C22×C3×C5C22×D314yes—
79C22×C3×C5C22×D3116yescomplemented
80C2×C5×D3—316no—
81C2×C5×D3—38no—
82C2×C5×D3—316no—
83C2×C5×D3—664no—
84C2×C5×D3—616no—
85C3×C4×C5C22×D318yescomplemented
86C5×Dic3—38no—
87C23×D3—38no—
88C2×C3×D4C5×D314yescomplemented
89C2×#67—38no—
90D3×D4—332no—
91C2×D12—34no—
92C2×C4×D3—34no—
93C32×C5C22×D411yescharacteristic, complemented, Hall
94C23×C5—91no—
95C23×C5—92no—
96C23×C5—98no—
97C23×C5—188no—
98C23×C5C2×C3⋊D312yescomplemented
99C5×D4—98no—
100C5×D4—94no—
101C5×D4C2×C3⋊D314yesdirect product factor
102C2×C4×C5—91no—
103C2×C4×C5—94no—
104C2×C4×C5C2×C3⋊D311yescharacteristic, complemented
105C22×C32—24no—
106C22×C32C23×C511yescharacteristic
107C22×C32C23×C514yescomplemented
108C2×C3⋊D3—24no—
109C2×C3⋊D3—216no—
110C2×C3⋊D3C5×D414yesdirect product factor
111C2×C3⋊D3C23×C512yes—
112C2×C3⋊D3C23×C514yescomplemented
113C32×C4C23×C512yescomplemented
114C3⋊Dic3C23×C512yescomplemented
115C22×D4—91noSylow
116C2×C3×C5—216no—
117C2×C3×C5D3×D418yescomplemented
118C2×C3×C5C23×D314yes—
119C5×D3—316no—
120C5×D3—616no—
121C23×C3C2×C5×D318yescomplemented
122C22×D3—34no—
123C22×D3—38no—
124C22×D3—332no—
125C22×D3—632no—
126C3×D4C2×C5×D3116yescomplemented
127C2×C3×C4C2×C5×D314yescomplemented
128#67—332no—
129C2×Dic3—34no—
130D12—316no—
131C4×D3—316no—
132C22×C5—24no—
133C22×C5—92no—
134C22×C5—94no—
135C22×C5—94no—
136C22×C5—1816no—
137C22×C5—184no—
138C22×C5C22×C3⋊D311yescharacteristic
139C22×C5C22×C3⋊D314yescomplemented
140C4×C5—92no—
141C4×C5C22×C3⋊D312yescomplemented
142C2×C32—24no—
143C2×C32C2×C5×D412yescomplemented
144C2×C32C24×C511yescharacteristic
145C3⋊D3—24no—
146C3⋊D3C2×C5×D414yesdirect product factor
147C24—92no—
148C2×D4—92no—
149C2×D4—98no—
150C2×D4—91no—
151C2×D4C5×C3⋊D311yescharacteristic, direct product factor
152C22×C4—91no—
153C3×C5C2×D3×D414yescomplemented
154C22×C3—216no—
155C22×C3C22×C5×D314yes—
156C22×C3C22×C5×D3116yescomplemented
157C2×D3—316no—
158C2×D3—38no—
159C2×D3—316no—
160C2×D3—664no—
161C2×D3—616no—
162C3×C4C22×C5×D318yescomplemented
163Dic3—38no—
164C2×C5—24no—
165C2×C5—94no—
166C2×C5—184no—
167C2×C5D4×C3⋊D312yesdirect product factor
168C2×C5C23×C3⋊D311yescharacteristic
169C32C22×C5×D411yescharacteristic, complemented, Sylow
170C23—91no—
171C23—92no—
172C23—98no—
173C23—188no—
174C23C2×C5×C3⋊D312yescomplemented
175D4—98no—
176D4—94no—
177D4C2×C5×C3⋊D314yesdirect product factor
178C2×C4—91no—
179C2×C4—94no—
180C2×C4C2×C5×C3⋊D311yescharacteristic, complemented
181C2×C3—216no—
182C2×C3C5×D3×D418yescomplemented
183C2×C3C23×C5×D314yes—
184D3—316no—
185D3—616no—
186C5C2×D4×C3⋊D311yescharacteristic, direct product factor, Sylow
187C22—24no—
188C22—94no—
189C22—92no—
190C22—94no—
191C22—1816no—
192C22—184no—
193C22C22×C5×C3⋊D311yescharacteristic
194C22C22×C5×C3⋊D314yescomplemented
195C4—92no—
196C4C22×C5×C3⋊D312yescomplemented
197C3C2×C5×D3×D414yescomplemented
198C2—24no—
199C2—94no—
200C2—184no—
201C2C5×D4×C3⋊D312yesdirect product factor
202C2C23×C5×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C5C22×C3⋊D3
commutator, cosocleC2×C32C24×C5
FrattiniC2C23×C5×C3⋊D3
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C5×D4C3⋊D3
hypocenterC32C22×C5×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×C5×C3⋊D3C2semidirect
2. C2×C32×C5×D4C2semidirect
3. C2×C5×#638C2semidirect
4. C5×D4×C3⋊D3C2direct (N × H)
5. C2×C5×C4⋊(C3⋊D3)C2semidirect
6. C2×C4×C5×C3⋊D3C2semidirect
8. C23×C32×C5C22semidirect
11. C22×C5×C3⋊D3C22semidirect
12. C22×C5×C3⋊D3C22semidirect
13. C32×C5×D4C22semidirect
14. C2×C32×C4×C5C22semidirect
15. C5×#638C22semidirect
16. C2×C5×C3⋊Dic3C22semidirect
17. C5×C4⋊(C3⋊D3)C22semidirect
18. C4×C5×C3⋊D3C22semidirect
19. C2×D4×C3⋊D3C5direct (N × H)
21. C2×C3×C5×D4D3semidirect
28. C22×C32×C5C23semidirect
31. C2×C5×C3⋊D3D4direct (N × H)
33. C2×C5×C3⋊D3C23semidirect
34. C32×C4×C5C23semidirect
35. C5×C3⋊Dic3C23semidirect
37. C23×C3⋊D3C2×C5semidirect
38. C2×C32×D4C2×C5semidirect
39. C2×#638C2×C5semidirect
40. D4×C3⋊D3C2×C5direct (N × H)
41. C2×C4⋊(C3⋊D3)C2×C5semidirect
42. C2×C4×C3⋊D3C2×C5semidirect
43. C23×C3×C5C2×D3semidirect
48. C3×C5×D4C2×D3semidirect
49. C2×C3×C4×C5C2×D3semidirect
56. C2×C32×C5C2×D4semidirect
59. C5×C3⋊D3C2×D4direct (N × H)
64. C2×C5×D4C3⋊D3direct (N × H)
66. C23×C32C22×C5semidirect
69. C22×C3⋊D3C22×C5semidirect
70. C22×C3⋊D3C22×C5semidirect
71. C32×D4C22×C5semidirect
72. C2×C32×C4C22×C5semidirect
73. #638C22×C5semidirect
74. C2×C3⋊Dic3C22×C5semidirect
75. C4⋊(C3⋊D3)C22×C5semidirect
76. C4×C3⋊D3C22×C5semidirect
79. C22×C3×C5C22×D3semidirect
85. C3×C4×C5C22×D3semidirect
88. C2×C3×D4C5×D3semidirect
93. C32×C5C22×D4semidirect
98. C23×C5C2×C3⋊D3semidirect
101. C5×D4C2×C3⋊D3direct (N × H)
104. C2×C4×C5C2×C3⋊D3semidirect
107. C22×C32C23×C5semidirect
110. C2×C3⋊D3C5×D4direct (N × H)
112. C2×C3⋊D3C23×C5semidirect
113. C32×C4C23×C5semidirect
114. C3⋊Dic3C23×C5semidirect
117. C2×C3×C5D3×D4semidirect
121. C23×C3C2×C5×D3semidirect
126. C3×D4C2×C5×D3semidirect
127. C2×C3×C4C2×C5×D3semidirect
139. C22×C5C22×C3⋊D3semidirect
141. C4×C5C22×C3⋊D3semidirect
143. C2×C32C2×C5×D4semidirect
146. C3⋊D3C2×C5×D4direct (N × H)
151. C2×D4C5×C3⋊D3direct (N × H)
153. C3×C5C2×D3×D4semidirect
156. C22×C3C22×C5×D3semidirect
162. C3×C4C22×C5×D3semidirect
167. C2×C5D4×C3⋊D3direct (N × H)
169. C32C22×C5×D4semidirect
174. C23C2×C5×C3⋊D3semidirect
177. D4C2×C5×C3⋊D3direct (N × H)
180. C2×C4C2×C5×C3⋊D3semidirect
182. C2×C3C5×D3×D4semidirect
186. C5C2×D4×C3⋊D3direct (N × H)
194. C22C22×C5×C3⋊D3semidirect
196. C4C22×C5×C3⋊D3semidirect
197. C3C2×C5×D3×D4semidirect
201. C2C5×D4×C3⋊D3direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C5×C3⋊D32
C2×C32×C5×D42
C2×C5×#6382
C5×D4×C3⋊D32
C2×C5×C4⋊(C3⋊D3)2
C2×C4×C5×C3⋊D32
C2×C5×D3×D43
C2×D4×C3⋊D35